This invention relates to quartz crystal resonators. In a more particular aspect, this invention concerns itself with a family of doubly rotated quartz orientations, suitable for piezoelectric crystal resonators vibrating in c-mode resonance with turnover temperatures (T.sub.to) above 60.degree. C.
Piezoelectric crystal resonators find utility in a wide variety of electronic applications as a means for achieving a fixed frequency standard. They also find use for the same purpose in various time-pieces, such as wrist watches. Single crystal .alpha.-quartz is the most commonly used material for piezoelectric resonators, owing to its superior mechanical, physical and chemical properties. Quartz belongs to the trigonal crystal system, and material properties are crystal orientation dependent. The most important performance parameter of a crystal oscillator is the static frequency as a function of temperature, f(T), characteristic of the device. The normalized frequency offsets as a function of temperature may exhibit a maximum and a minimum. These positions are designated as the turnover temperatures, T.sub.to. For high stability applications, the resonator device is enclosed in a precisely controlled oven and maintained at T.sub.to. Most military applications specify upper environmental temperatures in the 60.degree. to 100.degree. C. range. The crystal orientation is selected to locate T.sub.to several degrees above the highest anticipated environmental temperature. Owing to T.sub.to sensitivity to crystallographic orientation, narrow angular tolerances, in order of minutes or seconds or arc, have to be maintained throughout the resonator fabrication process. Both requirements, precise oven control and crystal orientation, affect considerably oscillator costs. Certain orientations exist which have considerably smaller f(T) sensitivities than other directions. Typical examples include the standard AT-, BT-, and SC- cuts. The singly rotated AT- and BT-cut crystals are the most widely used orientations for high stability applications. The novel doubly rotated SC-cut orientation has considerably smaller temperature coefficient of frequency than the AT-cut. However, this order of magnitude improvement in performance is at the expense of an order of magnitude reduction in allowable crystal orientation tolerances.
As a consequence, a considerable research effort has evolved in an attempt to determine other crystal cuts that are less sensitive to crystallographic orientation than the currently utilized AT-cut, BT-cut, or SC-cut crystals. This research effort culminated in the discovery that novel combinations of phi and theta (.phi.,.theta.) angular orientations or cuts exist that yield turnover temperatures of 60.degree. C. and above, possess equivalent or better temperature-frequency characteristics than high precision AT-cut or BT-cut resonators; and, at the same time, are insensitive to crystallographic misalignments. For descriptive purposes, the novel crystal cut of this invention is referred to as the AK-cut.